I want to book a special swim with dolphins in cozumel that my cruise does not offer. My cruise offers swim with dolphins but My 2 kids want to do the royal swim which is a step above the swim with dolphins. Is it safe to go to Park with kids and not with the ship excursion?
Yes, Cozumel is a safe place. You won't have to do much of any walking off the beaten path. The taxis will pick you up in front of the ship/dock (large crowd of passengers) and take you directly to the park. And the same thing on the return trip. I wouldn't worry about it.
Just use the same level of caution you would going to a shopping mall and you should be fine.
We were in Cozumel on Thursday (yes, we got off the ship this morning--tears). Our guide, a resident now but originally from Oregon, had us leaving our snorkeling gear and assorted flotsum of belongings in an open jeep while we were in a restaurant, tavern, and beach areas. He says they have virtually no crime there. Not sure I was that confident but the guy has lived there six years . . . We did the Royal swim on our own 3 years ago. It was a blast! the park is an easy 10 minute taxi ride--not even 5 K if I were to guess from most of the piers. It was easy (we had two kids along as well.) Take a water camera. Remember that Cozumel is on Central time, if you sail out of Miami you will probably be on Eastern (ship's time)so plan for arrivals and departures accordingly. Also we were in port by 10:00 as expected on our itinery, but Mexican officials did not clear the ship until 10:30. We still made a 10:45 rendevous with our guide, but don't cut things too close for your "appointed" time.
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Sproheat is correct in that customs clearance can sometimes take longer than you think, so be aware of that if you set up any prearranged tours. BUT having said that, most tour guides understand that you will get of the ship as quickly as allowed and won't leave unless it is clear you are not coming (hours)
If you book something, just verify with the guide that he will wait for you to get off the ship and that you will meet him as soon as you are allowed off the ship.